Adaptive Generation Method for Small Volume Easy Fabrication Freeform Unobscured Three-Mirror Systems Based on Machine Learning

Freeform unobscured multiple-mirror systems have been widely applied in high-precision optical fields due to their high imaging quality and no chromatic aberration and central obstruction. However, how to design a freeform unobscured multiple-mirror system with small system volume, imaging quality, and low manufacturing difficulty is challenging. This study proposes an adaptive generation method for freeform unobscured three-mirror systems with small volume and ease of fabrication based on machine learning, considering the fabrication constraints, volume limitations, imaging quality, and design efficiency. First, an error function based on volume, fabrication, and imaging quality functions is constructed, and a dataset is generated using this error function. Then, a machine learning model is trained using this dataset, enabling efficient prediction of the parameters for small-volume, easy-to-fabricate freeform unobscured three-mirror systems. Finally, the parameters of the freeform unobscured three-mirror system are predicted using the trained model, and combined with the freeform surface generation method, a freeform unobscured three-mirror imaging system is automatically obtained. Experimental results demonstrate that our method can effectively generate freeform unobscured three-mirror systems that meet the requirements for small volume and easy fabrication, providing a new approach for optical design.